Discrete & Continuous Probability distribution in R studio
Modules Required
To work with discrete probability distributions in R, the following packages are required:
e1071– Provides various statistical and machine learning functions.distr– Used for handling probability distributions.
The installation and removing packages can be done with GUI as well.
Installing Required Packages
To install the required packages, run:
install.packages("e1071")
install.packages("distr")Loading Packages
After installation, load the packages using:
library(e1071)
library(distr)Removing Packages (After Use)
To unload a package from memory:
detach("stats", unload = TRUE)Concepts Covered
- Working with discrete probability distributions.
- Calculating probability mass function (PMF).
- Finding the distribution function, quantiles, and generating random samples.
- Computing expected values.
- Solving probability equations using root-finding methods.
- Transforming random variables.
Functions Used
Discrete Probability Distribution Functions
The distr package provides the following functions to work with discrete data:
| Function | Description |
|---|---|
ddiscrete(x, probs, values = 1:length(probs)) | Computes the probability mass function (PMF) of a discrete distribution. |
pdiscrete(q, probs, values = 1:length(probs)) | Computes the cumulative distribution function (CDF). |
qdiscrete(p, probs, values = 1:length(probs)) | Computes the quantile function (inverse of CDF). |
rdiscrete(n, probs, values = 1:length(probs), ...) | Generates n random samples from a discrete distribution. |
Parameters
| Parameter | Description |
|---|---|
x, q | A vector or array of quantiles. |
p | A vector or array of probabilities. |
n | The number of observations (random samples to generate). |
probs | The probability values associated with each outcome. The sum must be 1. |
values | The possible values of the discrete distribution. |
... | Additional arguments (ignored for compatibility). |
These functions allow us to work with discrete distributions where the probability of each value is proportional to the probs parameter.
Example 1: Creating a Discrete Probability Distribution
To define a discrete probability distribution and compute the expected value:
X <- c(0, 1, 2, 3, 4) # Possible values
P <- c(0.1, 0.15, 0.2, 0.55) # Corresponding probabilities
# Compute XP (value * probability)
XP <- X * P
# Create a data frame for better visualization
data.frame(X, P, XP)
# Compute the expected value (mean)
mean_value <- sum(XP)
print(mean_value)Example 2: Finding a Missing Probability Value
To find a missing probability in a probability distribution, convert it into a root-finding problem.
For example, to solve 0.6 + 6x = 1 for x:
f <- function(x) (0.6 + 6*x - 1)
root_value <- uniroot(f, lower=0, upper=1)$root
print(root_value)Example 3: Computing the Distribution of a Transformed Variable
If Y = g(X), we can compute the probability distribution of Y using transformations.
For instance, if Y = 2X + 1 for a given discrete distribution, we can derive its probabilities accordingly.
References
- This note is AI Generated with human modifications.
Information
- date: 2025.03.12
- time: 16:50